J. Phys. Chem. A 2002, 106, 9065-9070
9065
Comparative G2(MP2) Molecular Orbital Study of B3H7XH3 and H3BXH3 Donor-Acceptor Complexes (X ) N, P, and As) A. Es-sofi,† C. Serrar,† A. Ouassas,† A. Jarid,*,† A. Boutalib,*,† I. Nebot-Gil,‡ and F. Toma´ s‡ De´ partement de Chimie, UniVersite´ Cadi Ayyad, Faculte´ des Sciences Semlalia, B.P. 2390 Marrakech, Morocco, and Institut de Cie` ncias Molecular (Departament de Quı´mica Fı´sica), UniVersitat de Vale` ncia, Dr. Moliner, 50 E-46100 Burjasot, Vale` ncia, Spain ReceiVed: April 17, 2002; In Final Form: July 11, 2002
B3H7XH3 and H3BXH3 (X ) N, P, and As) have been studied as donor-acceptor complex type at the G2(MP2) level of theory. Both single- and double-bridged structures of B3H7 Lewis acid are taken into account. Although the double-bridged structure is energetically favored in the isolated state, the coordination prefers the single-bridged one. The monoborane adducts adopt the staggered arrangement with C3V symmetry. The energetic analysis by natural bond orbital theory shows that the decrease of hyperconjugative contribution upon complexation in the B3H7 moiety has, as consequence, a loss of symmetry for B3H7XH3 (X) P and As) complexes. In the two series, the coordination is the result of two opposing interactions. The first one is stabilizing, developed between a′ symmetry fragment molecular orbitals, and is mainly of 3MO-4e nature. The second one is destabilizing and developed between occupied molecular orbitals (2MO-4e) of donor and acceptor fragments having a′′ symmetry. Furthermore, in the case of BH3 complexes, the complexation is made along the C3 axis that joined the two fragments, whereas for B3H7, it is mainly centered on the nonequivalent boron atom, but the two other ones are also weakly involved in the coordination through a suitable p orbital even if the donor fragment is not on the three boron triangle center.
1. Introduction A typical property of electron-deficient boranes is their Lewis acidity, which reflects the fact that boron possesses fewer valence electrons than valence orbitals;1 they react readily with a range of Lewis bases in both solution and gas phase. However, this property differs from small boranes to higher borane clusters because the boron connectivity increases when the number of borons in the clusters increases. Indeed, the structural chemistry of higher boranes is dominated by deltrahedra, cluster shapes composed of numerous triangles formed with three boron atoms. Thus, it’s more interesting to compare the complex stability formed by reaction of monoborane (BH3) and triborane (B3H7) with Lewis bases such as NH3, PH3, and AsH3. The stability and properties of BH3L complexes (L ) Lewis base) are sufficiently studied2-18 and carried out. In the case of those Lewis acid-base complexes, it was shown that the stability of the formed donor-acceptor adducts depends on the nature of the ligand and BH3 acid substituent. Therefore, Anane et al.17,18 have shown that the complexes formed with BH3 and XH3 (X ) P and N) are found to be more stable than those obtained with XH2 (X ) O and S) than with XH (X ) F and Cl) at the G2 level of theory. They have also shown that H3BNH3 is more stable than H3BPH3 and that the s character of the B-X bond decreases and p character increases as the electronegativity of X increases. They have concluded that the B-X bond cannot be treated only in terms of a simplest HOMO-LUMO interaction model (two level and two electron model system: 2MO-2e), but the interaction occurs between two molecular orbitals of the acceptor (LUMO and a deeper † ‡
Universite´ Cadi Ayyad. Universitat de Vale`ncia.
orbital) and the highest occupied molecular orbital (HOMO) of the donor (a three level and four electron model system: 3MO-4e). They have also illustrated that the complexation energies depend on the degree of substitution on the acceptor and donor fragments. In recent studies, our group19,20 has investigated H3AlXR3 (X ) N, P, and As, R ) H and Me) as donor-acceptor complex types at the G2(MP2) level of theory. The stability of these complexes decreases when going from nitrogen to arsenic, and the evolution of the complexation energy of H3AlXR3 adducts depends on the coordination mode; this is a result of two interaction types: a stabilizing interaction between a1 symmetry fragment molecular orbitals and a destabilizing interaction between e ones. The stability of donor-acceptor complexes formed by B3H7 borane as Lewis acid and different Lewis bases is not sufficiently studied. However, the stability of isolated B3H7 conformations was largely carried out. In fact, Lipscomb et al.21 have shown that the favored structure is that having two bridged hydrogen atoms (double-bridged: 2102 structure in styx notation22) compared to the structure with one bridged hydrogen atom (single-bridged: 1103 structure in styx notation) by above 4.4 kcal/mol. Experimentally, it was shown that the B3H7 moiety has only one bridged hydrogen in B3H7L (L ) NH3 and CO) compounds.23-25 Thus, when the ligand is removed, the B3H7 unit has a vacant orbital, which can be filled with some strain by conversion of a terminal hydrogen of the single-bridged structure to the double-bridged one. Morokuma et al.26 have investigated the stability and the structure of both B3H7NH3 and B3H7CO at the MP2/6-31G level of theory. They have shown that the B3H7 species in these complexes prefers the single-bridged arrangement. In continuation of our work, we now report our investigation of the B3H7XH3 (X ) N, P, and As) donor-acceptor complexes
10.1021/jp020981x CCC: $22.00 © 2002 American Chemical Society Published on Web 09/05/2002
9066 J. Phys. Chem. A, Vol. 106, No. 39, 2002
Es-sofi et al. TABLE 1: G2(MP2) Total Energies (in au) of B3H7XH3 Complexes single-bridged Cs
double-bridged C1
Cs
∆Ea
B3H7NH3 -134.971 627 -134.958 355 8.33 B3H7PH3 -421.174 055 -421.174 532 -421.154 637 12.44 B3H7AsH3 -2314.561 041 -2314.563 113 -2314.545 038 14.29 a ∆E (kcal/mol) is the difference in energy above the minimum energy conformation.
Figure 1. Optimized single- and double-bridged structures of isolated B3H7 borane.
compared to the H3BXH3 (X ) N, P, and As) ones. The relative stability of these complexes is examined with respect to the qualitative molecular orbital analysis (QMOA).27,28 To the best of our knowledge, no comparative study of these complexes has been carried out. 2. Computational Details Ab initio calculations were performed using the Gaussian 98 series of computer programs29 on the IBM RS/6000 workstations at the University of Vale`ncia. Geometry optimizations were performed at the MP2(full)/6-31G(d) level; the zero-point vibrational energies (ZPE) are obtained from scaled HF/6-31G(d) frequencies (scaled by the factor 0.893).30 For improved energy, the G2(MP2) energies31 were computed. The electronic structures have been done using the natural bond orbital (NBO)32 partitioning scheme at the MP2(full)/6-31G(d) level. NBOs are the localized set of easily recognizable Lewis-like (σ and π bond, lone pair, and core) and non-Lewis (σ* and π* antibond and Rydberg) orbitals, which are optimal in the sense of orthonormality and maximum occupancy of the Lewis set. An important feature of the NBO method is that unlike other charge partitioning schemes, the presence of diffuse functions in the basis sets does not significantly affect the result.32 On another hand, we did not correct for the basis set superposition errors (BSSE), which should be relatively small with a large basis set such as 6-311+G(3df,2p). Moreover, a study by Mikhali et al.,33 using the G2(+) method, and more recently a study by Mo and Gao34 show that the BSSE has little effect on the calculated complexation energies. 3. Results and Discussion 3.1. Geometries. First, we proceeded to the structural study of the series of B3H7NH3, B3H7PH3, and B3H7AsH3 compounds. Taking into account both C2V and Cs structural conformations of the B3H7 fragment (Figure 1), we made two corresponding approaches by imposing the Cs symmetry. Let us remember that
the double-bridged structure of isolated B3H7 is more stable than the single-bridged one.35,36 In this work, we have reexamined this stabilization; it is about 3.7 kcal/mol at the G2(MP2) level of theory. As we will show below, the LUMO that confers the Lewis acid property to B3H7 is localized on the B1 boron atom in both single- and double-bridged conformations. Nevertheless, this latter structure would be a bad acceptor via the B1 atom. In fact, if we compare these two structures, we note that B1 is not as accessible in the Cs double-bridged triborane as in the C2V single-bridged one. In the C2V conformation, the B1 atom is practically in a similar neighborhood to the BH3 simple system. Thus, we should expect a less-stable complexation when B3H7 adopts the double-bridged form than when it is in the singlebridged one. Effectively, the collected energetic data (Table 1) confirm it. We notice that for the three complexes, the singlebridged structure is more stable than the double-bridged one. Therefore, the energetic deviations are 8.33, 12.48, and 14.29 kcal/mol for B3H7XH3 (X ) N, P, and As, respectively) at the G2(MP2) level of theory. In previous works, only the singlebridged structure has been taken into account; the doublebridged one has been omitted for spectral24,25 and energetical26,37 considerations. In this work we also considered only the singlebridged structure. We then reoptimized the three single-bridged complexes B3H7XH3 (X ) N, P, and As) without symmetry constraints. In Figure 2, we have reported the favored conformations, which are all minima. In Table 2, we present selected bond lengths in isolated and complexed B3H7 borane. We remark that there are no important effects of the ligand coordination on the geometry of B3H7 Lewis acid. We notice that only the B3H7NH3 compound keeps Cs symmetry, whereas for the two other ones, the XH3 (X ) P and As) ligand is out of the symmetry plane. What are the factors behind these structural preferences? To answer this question, we have undertaken a NBO energetic analysis by carrying out interfragments zeroing interactions and Fock matrix elements deletions on B3H7 free and coordinated fragment. On another hand, the thorough examination of fragments’ donor and acceptor structural, and orbital interactions and coordination energy evolution within this series will permit, as we will see hereafter, us to confirm factors behind the choice of such geometrical preferences. 3.2. NBO Energetic Analysis. We considered free B3H7 and B3H7XH3 (X ) N, P, and As) compounds taken in their symmetries (C2V for free B3H7 and Cs for the others). We took only the symmetrical structures with the aim to know factors responsible for the fragment symmetry maintenance of the B3H7 fragment. This last could be regarded as being formed by a BH2 (Frag1) fragment and a H2B(H)BH2 (Frag2) one (Scheme 1). However, slight rotations of the Frag1 unit around the B1Hb C2 axis (bisector axis of HB1H angle) cause a symmetry loss. This symmetrical breaking is avoided thanks to, among other things, an electronic delocalization between B-H bonds (σ) of Frag1 unit and antibond lone pairs (LP*) of B1 and B2
Comparative G2(MP2) Molecular Orbital Study
J. Phys. Chem. A, Vol. 106, No. 39, 2002 9067 SCHEME 1
TABLE 3: HF/6-311G(d,p)//MP2(full)/6-31G(d) Deletion Energies (kcal/mol) Frag1-Frag2 LP(B3)-LP*(B1,2) compound zeroing deletion B3H7 B3H7NH3 B3H7PH3 B3H7AsH3
Figure 2. Optimized structures of B3H7XH3 (X ) N, P, and As) complexes.
TABLE 2: Selected Optimized Bond Lengths (Å) in Isolated and Complexed Single-Bridged B3H7 Borane distances
isolated B3H7
B3H7NH3a
B3H7PH3a
B3H7AsH3a
B1-B2 B2-B3 B1-Ht B2-Ht′
1.78 1.73 1.19 1.20
B2-Hb
1.34
1.84 1.71 1.20 1.19 1.20 1.32
1.84 1.73 1.20 1.19 1.20 1.31
1.84 1.73 1.20 1.19 1.20 1.31
a
The second value corresponds to equivalent hydrogen atoms.
atoms or between σ(B1,2-H) NBOs and LP (or LP*) ones of B1 atom. Those delocalizations are as much best as Frag1 B-H bonds are in the three-boron atoms plane. Two qualitative deletions have been considered. The first one is the Frag1 and Frag2 zeroing interaction. The corresponding energies could be considered close at this level of theory (Table 1). This interaction is a result of Lewis-Lewis and Lewis-non-Lewis Frag1 and Frag2 NBOs mixtures. The second deletion is the elimination of two Fock-matrix element sets that have a significant role in the Frag1-Frag2 interaction. However, the elimination of
510 475 515 513
408 323 265 275
σ(B3-H)-LP*(B1,2) and σ(B1,2-H)-LP*(B3) deletion 54 41 9 9
elements corresponding to LP(B1)-LP*(B1,2) shows that the corresponding interaction does not control the symmetry maintenance of the B3H7 moiety although its energy represents about 80%, 70%, and 50% of the total energy of the Frag1Frag2 interaction for B3H7, B3H7NH3, and B3H7XH3 (X ) P and As), respectively (Table 3). In fact, it is not too sensitive to the symmetry breaking by turning the Frag1 unit around the C2 axis. This interaction contributes to the three-centers twoelectron (3c-2e) bonding.1 The second deletion corresponds to sets of elements that ensure the σ(B-H) of one fragment and LP (or LP*) NBOs of boron atom of the other one. However, because this interaction implies out of three boron’s ring B-H bonds, its relative energy values give an idea of its capability to control the symmetry loss. The corresponding energy is about 54, 41, and 9 kcal/mol for free B3H7, B3H7NH3, and B3H7XH3 (X ) P and As), respectively and represents 11%, 9%, and 2% of the total Frag1-Frag2 interaction (Table 3). Starting from these values, we can already conclude that B3H7PH3 and B3H7AsH3 compounds are more likely to lose their symmetry than free B3H7 and B3H7NH3 ones. On the other hand, because the interacting NBOs are vicinal, we can also conclude that the symmetry breaking can be related, among other things, to the decrease of the hyperconjugative energetic contribution of Frag1-Frag2 interaction. A weak electrostatic or steric perturbation caused by the ligand could be sufficient to cause a symmetry breaking. 3.3. Structural Analysis. As we will show below, the complexation becomes weaker on going from NH3 to AsH3 fragments. However, the central atom of the donor fragment becomes increasingly bulky. This has the consequence of an increasing long distance B-X, so the donor fragment becomes increasingly mobile. Thus, small electrostatic or steric interactions could move it to one or the other side of its medium position. In Table 4, we have reported the net charges of the hydrogen atoms that are likely to interact with each other and distances that separate them. However, we note that, from the geometrical point of view, the distance dB1-X increases on going from N to As (1.63, 1.93, and 2.00 Å, respectively). This is normal because the atomic radius of the donor central atom increases in the even feel (0.74, 1.1, and 1.21 Å for N, P, and As, respectively).38 This has an effect on the distances between H(XH3) and H(B3H7) atoms, which increase, and thereafter, their interactions decrease. To illustrate this, we take dH1-H3 distance as an
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Es-sofi et al.
TABLE 4: MP2(full)/6-31G(d) B-X Bond Lengths (Å) and NBO Charges (e) of Interacting Hydrogens in Single-Bridged B3H7XH3 (X ) N, P, and As) Complexes B3H7NH3 Cs
B3H7PH3 Cs
B3H7AsH3
C1
Cs
C1
H1 H1′ H3 H3′
0.446 0.446 -0.010 -0.010
NBO Charges 0.032 0.038 0.032 0.035 0.003 0.003 0.003 -0.004
-0.020 -0.020 -0.024 -0.024
0.026 0.018 0.007 -0.008
dH1-H3 dH1-H3′ dH1′-H3′
2.21 3.16 2.21
Distances 2.66 2.76 3.71 2.88 2.66 2.73
2.70 3.81 2.70
2.97 2.65 2.71
TABLE 5: G2(MP2) Energies (au), Complexation Energies (kcal/mol), and MP2(full)/6-31G(d) B-X Bond Lengths (Å) of Single-Bridged B3H7XH3 and BH3XH3 Complexes, and Charge Transfer Qc (electron) complexes
energies
Ec
dB-X
Qc
B3H7NH3 B3H7PH3 B3H7AsH3 BH3NH3 BH3PH3 BH3AsH3
-134.971 627 -421.174 532 -2314.563 113 -83.022 744 -369.232 050 -2262.623 433
-31.80 -22.90 -14.80 -25.96 -21.10 -14.67
1.63 1.93 2.00 1.66 1.94 2.05
0.400 0.734 0.740 0.354 0.630 0.598
example (Table 4); we note that it increases from NH3 to AsH3 (2.21, 2.66, and 2.70 Å, respectively, in Cs symmetry and 2.21, 2.76, and 2.97 Å in C1 symmetry, respectively). In Cs symmetry, the H1 and H1′ atoms, on one hand, and H3 and H3′ atoms, on the other hand, are of like charge sign in the PH3 and AsH3 cases and oppositely charged in the NH3 one. Indeed, this symmetry imposes to H1-H3 and H1′-H3′ interactions the same intensities and same natures (repulsive or attractive). The B 3H7PH3 and B3H7AsH3 complexes are transition states and the B3H7NH3 complex is a minimum on the Cs symmetry potential surface. For the B3H7PH3 compound, in C1 symmetry, the rotation of the PH3 axis group around P-B1 and the P atom output from the median plane lead to a new geometrical repositioning of the H1 and H1′ atoms with respect to the H3 and H3′ ones (Figure 2). In fact, H3′ (negatively charged) moves to 2.88 and 2.73 Å from H1 and H1′, respectively, which are both positively charged, whereas H3 (positively charged) is at 2.76 Å from H1. Thus lateral double-attraction (H1-H3′ and H1′-H3′) and repulsion (H1-H3) take place and favor the C1 structure. We notice that this latter corresponds to a minimum in the total potential energy surface. The same remark can be made concerning the AsH3 complex (Figure 2 and Table 4). One can thus conclude that the interactions between these hydrogen atoms favor C1 symmetry for PH3 and AsH3 adducts and do not for the NH3 complex. Being given that, the attractive and repulsive interactions between hydrogen atoms in both cases have a decisive role in the structure choice. Let us note that although these interactions are weak, they affect the structural form solely if the coordination is also weak, that is, when the ligand is not strongly bound to the acceptor and could be easily moved out of its symmetrical position. This is confirmed by the low energy difference between the Cs structure and C1 one (0.30 and 1.33 kcal/mol at G2(MP2) level of theory for B3H7PH3 and B3H7AsH3, respectively (Table 1)) or by the complexation energy, which decreases from the corresponding NH3 compound to the AsH3 one (Table 5). Concerning the analogous compounds having BH3 as the acceptor, the staggered conformation is energetically favored with a perfect C3V symmetry. According to our reasoning and compared to B3H7 compounds, we would expect that there
Figure 3. Fragmental analysis of the “a′” symmetry molecular orbitals of (a) B3H7NH3, (b) B3H7PH3, and (c) B3H7AsH3.
would be no change concerning the symmetrical properties. This is especially controlled by atomic interactions between hydrogens. Indeed, each hydrogen atom of one fragment is exactly in the same geometrical environment as the two others, consequently the H(acceptor)-H(donor) interactions have the same intensity and the same nature. Contrary to B3H7 cases, this does not favor the symmetry reduction; thus all corresponding complexes kept the staggered C3V symmetry.
Comparative G2(MP2) Molecular Orbital Study
J. Phys. Chem. A, Vol. 106, No. 39, 2002 9069
Figure 4. “a′′” symmetry MO energy level diagram for B3H7 and XH3 (X ) N, P, and As).
3.4. Qualitative Molecular Orbitals Analysis. As we have mentioned in the Introduction, we showed that there are two interaction types that manage the AlH3 complexation with NH3, PH3, and AsH3.19 In the present work, the same remarks have been noted for the BH3XH3 (X ) N, P, and As) complexation. The first one is stabilizing and occurs between the higher a′ molecular orbitals of both donor and acceptor fragments, whereas the second one occurs between a′′ ones. This latter has a destabilizing character because its interacting orbitals are occupied. The coordination is a mixture of these two interactions but is globally stabilizing, and the evolution of the complexation energy is decreasing along the donor central atom column of the periodic table from N to As. Similarly to the BH3 adducts case, the B3H7XH3 (X ) N, P, and As) coordination is governed by stabilizing and destabilizing interactions. The first one is the seat of a mixture between a′ molecular orbitals of both acceptor and donor fragments. In this interaction, the acceptor fragment principally participates in the LUMO. Another orbital is also concerned by this interaction; it is that developed on both p atomic orbitals implying in the four B-H bonds of BH2 bridged fragments (Figure 3). However, although the coordination of the two Lewis acids (BH3 and B3H7) is almost the same from the energetic point of view, their coordination mode is different because B3H7 involves the three boron atoms. In fact, for the BH3 Lewis acid, the complexation is made perfectly along the C3 axis that joins the two fragments, whereas for the B3H7 one, while it is mainly centered on B1 boron atom, the two, B2 and B3, others also are involved through a suitable p orbital. Nevertheless, the donor fragment is not on the B1B2B3 triangle center (Figure 2). The donor molecular orbital analysis brings out a weak difference concerning a′ MOs, which is implied in the stabilizing interaction. This difference has an important consequence on the complexation energy evolution along the column of the periodic table corresponding to the central atom of the donor fragment. In fact, the NH3 donor participates only by the 4a′ HOMO, whereas PH3 and AsH3 participate by the na′ HOMO and (n - 2)a′ (n ) 7 and 13, respectively). This latter MO is so much energetically deeper in the NH3 fragment that it does not affect the 3MO-4e stabilizing mixture of B3H7NH3 interaction, whereas in the two other compounds, its energy position enables it to intervene in this interaction. Having a perturbational role (destabilizing), these molecular orbitals unfavorably act in the coordination process and have a consequence on the complexation energy evolution despite the similarity of the coordination mode within this series. Concerning the second interaction, it occurs between the occupied a′′ MO of both fragments. Having 2MO-4e character,
this interaction is destabilizing and disfavors the coordination (Figure 4). The energetic position of the XH3 donor fragment a′′ molecular orbital becomes closer to those of the acceptor and, consequently, the destabilizing interaction becomes stronger with the series (N, P, and As). Nevertheless, the destabilizing interaction is lower than the first stabilizing one because the complexation is energetically confirmed. As we have mentioned before, those two mixtures have an influence on the coordination energy variation within the two series of B3H7XH3 and BH3XH3 (X ) N, P, and As). In Table 5, we notice that for B3H7, as for BH3 acceptor compounds, the complexation energy decreases on going from NH3 to AsH3 adducts. This evolution does not agree with the HOMO of one of the donors, which becomes energetically close to the vacant orbital of the acceptor, which would lead one to believe that the coordination becomes strong in this direction. The destabilizing interaction increases more quickly, within these two sets from NH3 to AsH3, than the stabilizing one. This results therefore in a decreasing and no regular evolution of the complexation energy. Finally, by analyzing NBO charge evolution (Table 5), we can conclude that generally, there is no correlation between the complexation energy and the charge transfer for the same Lewis acid. Nevertheless, we notice that the increase of the transferred charge contributes to the stability of B3H7XH3 (X ) N, P, and As) complexes according to their homologous BH3XH3, respectively. 4. Conclusion Both B3H7 and BH3 borane Lewis acid complexes with electron donors such as XH3 (X ) N, P, and As) depend on two types of interaction (stabilizing and destabilizing). The first one is ensured by the HOMO(donor)-LUMO(acceptor) mixture, which is weakly perturbed by an occupied a′ molecular orbital intervention of the acceptor, leading to a 3MO-4e system. The latter perturbation acts unfavorably to the coordination. Another occupied a′ molecular orbital of the donor also acts against the formation of the complex especially in the PH3 and AsH3 cases. With regard to the strongly destabilizing mixture between the occupied a′′ orbitals, it becomes increasingly strong on going from NH3 to AsH3 because the corresponding interacting orbitals become energetically close. The complexation is a result of those four interactions of which the stabilizing one is the prevailing. The decreasing evolution of the complexation energy is due to the increased variation of the destabilizing interactions in comparison with the stabilizing one. Furthermore, the complexation of B3H7 is mainly made on the nonequivalent boron atom, and the two others also are
9070 J. Phys. Chem. A, Vol. 106, No. 39, 2002 weakly implied, but the acceptor-donor bond is not on the axis of the three boron atom ring. Confirmed by the NBO energetic analysis and NBO charge calculations, the interaction of any hydrogen atoms of both fragments and the lowering of hyperconjugative contribution in B3H7 fragment are responsible for the symmetry breaking in B3H7PH3 and B3H7AsH3 adducts. Acknowledgment. This work was partially supported by the Program de Coope´ration Interuniversitaire Maroco-Espagnol (Project 52P-00). References and Notes (1) Lipscomb, W. N. Boron hydrides; Benjamin: New York, 1963. (2) Stock, A.; Massenz. C. Chem. Ber. 1912, 45, 3539. (3) Mutterties, E. Boron Hydrides Chemistry; Academie Press: New York, 1975. (4) Lane, C. F. Chem. ReV. 1976, 76, 773. (5) Carpenter, J. D.; Ault, B. S. J. Phys. Chem. 1991, 95, 3502. (6) Carpenter, J. D.; Ault, B. S. J. Mol. Struct. 1993, 298, 17. (7) Carpenter, J. D.; Ault, B. S. J. Phys. Chem. 1992, 96, 7913. (8) Carpenter, J. D.; Ault, B. S. J. Phys. Chem. 1991, 95, 3507. (9) Carpenter, J. D.; Ault, B. S. J. Phys. Chem. 1992, 96, 4288. (10) Carpenter, J. D.; Ault, B. S. J. Phys. Chem. 1993, 97, 3697. (11) Sakai, S. J. Phys. Chem. 1995, 99, 9080. (12) Umeyama, H.; Morokuma, K. J. Am. Chem. Soc, 1976, 98, 7208. (13) Glendening, E. D.; Streitwieser, A. J. Chem. Phys. 1994, 100, 2900. (14) Jonas, V.; Frenking, G.; Reetz, M. T. J. Am. Chem. Soc. 1994, 116, 8741. (15) Dapprich, S.; Frenking, G. J. Phys. Chem. 1995, 99, 9352. (16) Skancke, A.; Skancke, P. N. J. Phys. Chem. 1996, 100, 15079. (17) Anane, H.; Boutalib, A.; Tomas, F. J. Phys. Chem. A 1997, 101, 7879. (18) Anane, H.; Jarid, A.; Boutalib, A.; Nebot-Gil, I.; Tomas, F. Chem. Phys. Lett. 1998, 296, 277. (19) Anane, H.; Jarid, A; Boutalib, A. J. Phys. Chem. A 1999, 103, 9847. (20) Boutalib, A.; Jarid, A.; Nebot-Gil, I.; Tomas, F. J. Phys. Chem. A 2001, 105, 6526. (21) Mckee, M. L.; Lipscomb, W. N. Inorg. Chem. 1982, 21, 2846.
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